In the field of acoustic well logging a tool is used wherein a sonic pulse transmitter and a sonic receiver are spaced axially along the borehole. Frequently, a plurality of sonic receivers are employed to improve the precision with which information can be obtained about the borehole and the earth formation around it.
When an acoustic pulse is generated by a transmitter, a complex acoustic wave train is produced. The acoustic waves travel both radially from the borehole into the formation and axially towards the sonic receiver or multiple receivers as the case may be. The sonic receivers include transducers whose outputs are electrical waveforms representative of the acoustic waves incident upon the receivers. Suitable amplifiers are employed to provide amplified waveforms for borehole investigation.
Reference is made to a 1963 publication in which the order of wave arrivals is described and separate waves identified. The article was presented at the Thirtieth Annual Fall Meeting of the Society of Petroleum Engineers of the American Institute of Mining, Metallurgical and Petroleum Engineers in New Orleans, Oct. 6-9, 1963 and is entitled "The Use of Compressional and Shear Acoustic Amplitudes for the Location of Fractures" by R. L. Morris, D. R. Grine and T. E. Arkfeld.
The acoustic waves incident upon the receivers usually arrive in the order of their respective velocities. Hence, for a transmitter-receiver spacing which is substantially greater than the borehole diameter, the wave arrivals in an open or uncased hole, are at first early arrivals such as the compressional wave, followed by a shear wave, a pseudo Raleigh wave and a direct-mud wave. These early arrival waves, in turn, are followed by so-called later arriving or low velocity waves such as the Stoneley and the tube waves. In a cased hole, the casing signal, or that portion of the acoustic energy traveling through the casing may be first to arrive. Depending upon the type of formation, the shear wave may arrive after the direct or mud arrival.
The term "late arrival" or "late arriving wave" as used herein refers to a sonic wave having a velocity which is less than the direct or mud wave. It has been discovered that such late arriving wave is further characterized by its energy-frequency excitation and that its excitation in a borehole may be enhanced at low frequencies or at a sonic wavelength .lambda. which is of the order of or significantly larger than the borehole diameter d, or .lambda. &gt;&gt; d.
A late arrival such as the Stoneley wave would be characterized in a perfectly elastic medium with a uniform energy distribution across the borehole and a theoretical amplitude response which varies exponentially and inversely with frequency from a minimum at high frequencies to a maximum at low frequencies. In such perfect medium there should be no attenuation of any frequency with distance for the Stoneley wave. At some frequencies the Stoneley wave is dispersive in nature and its phase velocity varies with frequency.
The entire acoustic waveform from a short spacing receiver has a complex appearance by virtue of various factors such as inadequate time to obtain wave separations because of the limited spacing between the receiver and transmitter, the different decay times for the different arrivals, the presence of reflections in the borehole, the duration and spectrum of the sonic pulse generated by the transmitter and the detection and transfer function of the sonic receiver system. Added to these factors are the variations imposed by the media one seeks to investigate such as the formation and the borehole.
One may, for example, in conjunction with other logging information, construct an elastic model of the formation being investigated. Variations between the elastic model parameters and those measured from an acoustic borehole investigation of the later arrivals as disclosed herein may then be used to derive significant characteristics such as the degree of compaction, fracturing and vugular formation. Both early and late arrivals may contribute useful information; hence, the entire acoustic waveform produced by a sonic receiver in response to a sonic transmitter pulse can be of interest.
The earliest arriving waves in the acoustic waveform have been extensively used to derive information about the borehole medium, whether this be the formation around the borehole or the quality of the cement bonding in a cased borehole. In cement bonding evaluation, variations in amplitude of an early wave arrival such as the casing signal is monitored. The transit time or velocity of waves such as the formation compressional wave and shear wave are frequently measured by detecting these waves in the waveforms of sequentially spaced sonic receivers. In a copending patent application entitled "Method and Apparatus for Determining Acoustic Wave Parameters for Well Logging" filed on May 27, 1975 by the same inventor as for this invention and assigned to the same assignee, an accurate and reliable technique for determining the transit times is described, for example, for the compressional and shear waves.
It is frequently desired to determine the shear modulus, .mu..sub.2, of the formation. This elastic parameter may be directly determined from a knowledge of the velocity of the shear wave, V.sub.s, by the relationship .mu..sub.2 = .rho.V.sub.s.sup.2 where .rho. is the density of the formation and may be derived from a density log. The velocity of the shear wave, however, is not always convenient to measure, particularly when the shear wave velocity is about equal or less than the fluid or direct mud wave velocity. The shear wave frequently is obscured by other arrivals and of smaller magnitude than the earlier arriviing compressional wave. Accordingly, a direct measurement of the shear wave is not always practical and other approaches for the determination of the shear modulus of the formation are needed.
The prior art includes numerous publications which make reference to later arrival waves in an acoustic waveform. In an early publication by M. A. Biot, entitled "Propagation of Elastic Waves in a Cylindrical Bore Containing a Fluid," published in the Journal of Applied Physics, Vol. 23, No. 9, September 1952, pages 997-1005, the behavior of a later arrival wave such as the Stoneley wave is described.
Other publications dealing with late arriving waves have been made, such as in U.S. Pat. No. 3,127,950 by O. A. Itria for a method of determining shear wave velocities by employing a large transmitter-receiver spacing to obtain measurements of the velocity of a tube wave and the densities of the borehole fluid and the formation surrounding the borehole. Time separation and attenuation inherent to considerable transmitter-receiver spacing are employed by Itria together with a gating circuit to reject unwanted earlier wave arrivals.
Acoustic transmitters for producing sonic pulses containing low frequencies have been described in the art for investigating early arrivals particularly in cased holes (see U.S. Pat. No. 3,909,775 to J. C. Lavigne). Note, for example, an April 1966 article by Chaney et al published in the Journal of Petroleum Technology on page 407 and entitled "Some Effects of Frequency Upon the Character of Acoustic Logs." As described in this latter article, compressional amplitude studies are improved by the elimination of frequencies between 20 KHz and 50 KHz from the effective pulse spectrum. In British Patent No. 1,176,350 sonic pulses with spectra of from 2 KHz to about 20 KHz are described as useful to derive information related to the permeability of earth formation. A low frequency transducer for generating acoustic energy above 75db level for a bandwidth from 2.4 KHz to 9.6 KHz is described in U.S. Patent to Holloway, U.S. Pat. No. 3,845,333.
The use of late arrival waves such as the Stoneley wave in borehole investigations requires a convenient practical method for exciting and extracting such wave. In order to enhance the generation of Stoneley waves, it is desirable to emphasize those parameters of a well logging tool needed to excite and enable extraction of the Stoneley wave over a broad range of lithology conditions.
Frequency analyses have been proposed for waveforms representative of sonic waves to identify the amplitudes of different frequencies. See, for example, the U.S. Patent to Moore, U.S. Pat. No. 3,588,800 wherein a borehole investigation technique is described using a spectrum analyzer responsive to waveforms. The measured amplitude of different frequency segments are used to drive information about the earth formation. A frequency spectrum analysis beginning at about 30 KHz and extending to about 200 KHz is taught to be useful for the earth formation analysis.
In the U.S. Patent to Beil, U.S. Pat. No. 3,747,702, a sonic waveform spectrum analysis technique is described for evaluating the quality or effectiveness of the cement in a cased borehole. Early arriving waves in acoustic waveforms may be examined with three adjustable passband filters to determine the cement condition. The center bands of the filters are selected on the basis of the size of the casing. The frequency range is selected sufficiently wide from about 10 KHz to about 35 KHz range to enable the examination of early arrivals such as the compressional and determined sonic wave reflection coefficients.
A difficulty in extracting a late arrival may be caused by relatively long lasting transmitter sonic pulses. These long pulses tend to produce wave interferences at the receiver between persisting early arrivals and beginning late arrivals at least with commonly employed transmitter-receiver spacings. Improved wave separation, and thus less wave interference can be obtained by increasing the transmitter-receiver spacing but at the expense of a loss in amplitude of the early arrivals. Since it is preferred to preserve the early arrivals as well as the late arrivals, special techniques are needed to generate, extract and employ both the early and late arrivals in the entire wavetrain.